A circle has a circumference of $10\pi$. It has an arc of length $\dfrac{39}{4}\pi$. What is the central angle of the arc, in degrees? ${10\pi}$ ${351^\circ}$ $\color{#DF0030}{\dfrac{39}{4}\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{s}{c}$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{39}{4}\pi \div 10\pi$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{39}{40}$ $\theta = \dfrac{39}{40} \times 360 ^ \circ$ $\theta = 351^\circ$